J. Carrillo, M.P. Gualdani, A. Jüngel:

"Convergence of an entropic semi-discretization for nonlinear Fokker-Planck equations in R^d";

Publicacions Matemàtiques,52(2008), 413 - 433.

A nonlinear degenerate Fokker-Planck equation in the whole space

is analyzed. The existence of solutions to the corresponding

implicit Euler scheme is proved, and it is shown that the

semi-discrete solution converges to a solution of the continuous

problem. Furthermore, the discrete entropy decays monotonically in

time and the solution to the continuous problem is unique. The

nonlinearity is assumed to be of porous-medium type. For the

(given) potential, either a less than quadratic growth condition

at infinity is supposed or the initial datum is assumed to be

compactly supported. The existence proof is based on

regularization and maximum principle arguments. Upper bounds for

the tail behavior in space at infinity are also derived in the

at-most-quadratic growth case.

Siehe englischen Abstract.

Fokker-Planck equation, drift-diffusion equation, degenerate parabolic equation

Created from the Publication Database of the Vienna University of Technology.